Posterior sampling with Adaptive Gaussian Processes in Bayesian parameter identification Article Swipe
Paolo Villani
,
Daniel Andrés-Arcones
,
Jörg F. Unger
,
Martin Weiser
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.17858
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.17858
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many more evaluations of the forward model. Replacing computationally expensive forward models by fast surrogate models is an attractive option. However, computing the simulated training data for building a sufficiently accurate surrogate model can be computationally expensive in itself, leading to the design of computer experiments problem of finding evaluation points and accuracies such that the highest accuracy is obtained given a fixed computational budget. Here, we consider a fully adaptive greedy approach to this problem. Using Gaussian process regression as surrogate, samples are drawn from the available posterior approximation while designs are incrementally defined by solving a sequence of optimization problems for evaluation accuracy and positions. The selection of training designs is tailored towards representing the posterior to be sampled as good as possible, while the interleaved sampling steps discard old inaccurate samples in favor of new, more accurate ones. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs.
Related Topics
Concepts
Bayesian probability
Posterior probability
Identification (biology)
Gaussian
Sampling (signal processing)
Adaptive sampling
Computer science
Mathematics
Statistics
Algorithm
Artificial intelligence
Physics
Monte Carlo method
Biology
Computer vision
Botany
Quantum mechanics
Filter (signal processing)
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2411.17858
- https://arxiv.org/pdf/2411.17858
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4404990263
All OpenAlex metadata
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https://openalex.org/W4404990263Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2411.17858Digital Object Identifier
- Title
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Posterior sampling with Adaptive Gaussian Processes in Bayesian parameter identificationWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2024Year of publication
- Publication date
-
2024-11-26Full publication date if available
- Authors
-
Paolo Villani, Daniel Andrés-Arcones, Jörg F. Unger, Martin WeiserList of authors in order
- Landing page
-
https://arxiv.org/abs/2411.17858Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2411.17858Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2411.17858Direct OA link when available
- Concepts
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Bayesian probability, Posterior probability, Identification (biology), Gaussian, Sampling (signal processing), Adaptive sampling, Computer science, Mathematics, Statistics, Algorithm, Artificial intelligence, Physics, Monte Carlo method, Biology, Computer vision, Botany, Quantum mechanics, Filter (signal processing)Top concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.Numerical | 174 |
| abstract_inverted_index.Posterior | 0 |
| abstract_inverted_index.Replacing | 40 |
| abstract_inverted_index.available | 120 |
| abstract_inverted_index.computing | 16, 54 |
| abstract_inverted_index.estimates | 18 |
| abstract_inverted_index.expensive | 42, 69 |
| abstract_inverted_index.possible, | 157 |
| abstract_inverted_index.posterior | 23, 121, 150 |
| abstract_inverted_index.reduction | 179 |
| abstract_inverted_index.requiring | 32 |
| abstract_inverted_index.selection | 141 |
| abstract_inverted_index.simulated | 56 |
| abstract_inverted_index.surrogate | 47, 64 |
| abstract_inverted_index.accuracies | 85 |
| abstract_inverted_index.attractive | 51 |
| abstract_inverted_index.evaluation | 82, 136 |
| abstract_inverted_index.inaccurate | 165 |
| abstract_inverted_index.positions. | 139 |
| abstract_inverted_index.regression | 112 |
| abstract_inverted_index.surrogate, | 114 |
| abstract_inverted_index.evaluations | 35 |
| abstract_inverted_index.experiments | 78 |
| abstract_inverted_index.interleaved | 160 |
| abstract_inverted_index.significant | 178 |
| abstract_inverted_index.optimization | 25, 133 |
| abstract_inverted_index.representing | 148 |
| abstract_inverted_index.sufficiently | 62 |
| abstract_inverted_index.approximation | 122 |
| abstract_inverted_index.comprehensive | 9 |
| abstract_inverted_index.computational | 96, 182 |
| abstract_inverted_index.incrementally | 126 |
| abstract_inverted_index.computationally | 41, 68 |
| abstract_inverted_index.position-adaptive | 187 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |